(i) A black king
Total number of cards are 52
Number of black king cards = 2
Probability of getting black king cards is = Total number of black king cards/Total number of cards
= 2/52
= 1/26
∴ Probability of getting black king cards is 1/26
(ii) Either a black card or a king
Total number of cards are 52
Number of either a black card or a king = 28
Probability of getting either a black card or a king is = Total number of either black or king card/Total number of cards
= 28/52
= 7/13
∴ Probability of getting either a black card or a king is 7/13
(iii) Black and a king
Total number of cards are 52
Number of black and a king = 2
Probability of getting black and a king is = Total number of black and king card/Total number of cards
= 2/52
= 1/26
∴ Probability of getting black and a king is 1/26
(iv) a jack, queen or a king
Total number of cards are 52
Number of a jack, queen or a king = 12
Probability of getting a jack, queen or a king is = Total number of jack, queen or king card/Total number of cards
= 12/52
= 3/13
∴ Probability of getting a jack, queen or a king is 3/13
(v) Neither a heart nor a king
Total numbers of cards are 52
Total number of heart cards = 13
Probability of getting a heart is = Total number of hearts/Total number of cards
= 13/52
= 1/4
Total number of king cards = 4
Probability of getting a king is = Total number of king card/Total number of cards
= 4/52
= 1/13
Total probability of getting a heart and a king = 13/52 + 4/52 – 1/52
= (13+4-1)/52
= 16/52
= 4/13
∴ Probability of getting neither a heart nor a king = 1 – 4/13 = (13-4)/13 = 9/13
